Separating and Collapsing Results on the Relativized Probabilistic Polynomial-Time Hierarchy

Abstract

The probabilistic polynomial-time hierarchy 1990 is the hierarchy generated by applying the BP-operator to the Meyer-Stockmeyer polynomial-time hierarchy (PH), where the BP-operator is the natural generalization of the probabilistic complexity class BPP. The similarity and difference between the two hierarchies BPH and PH is investigated. Oracles A and B are constructed such that both PH(A) and PH(B) are infinite while BPH(A) is not equal to PH(A) at any level and BPH(B) is identical to PH(B) at every level. Similar separating and collapsing results in the case that PH(A) is finite having exactly k levels are also considered. © 1990, ACM. All rights reserved.